static public double AnalysisMethod(TypeKF typeKF, ScalarFunk1 f, double defA, double a, double b, double alpha, int n, double Eps)
{
double L = 2;
Vector vectorH = new Vector(3);
vectorH.data[1] = b - a;
vectorH.data[2] = (b - a) / L;
int countIter = 1;
double result = 0.0;
double tempR = Double.PositiveInfinity;
do
{
countIter++;
vectorH.data[0] = vectorH.data[1];
vectorH.data[1] = vectorH.data[2];
vectorH.data[2] = vectorH.data[1] / L;
//Эйткен
Vector vectorS = new Vector(3);
vectorS.data[0] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[0]);
vectorS.data[1] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[1]);
vectorS.data[2] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[2]);
double m = -Math.Log((Math.Abs(vectorS.data[2] - vectorS.data[1])) / (Math.Abs(vectorS.data[1] - vectorS.data[0]))) / Math.Log(L);
//Рижардсон
Matrix matrix_Cs_J = new Matrix(3);
for (int i = 0; i < matrix_Cs_J.N; i++)
{
for (int j = 0; j < matrix_Cs_J.N - 1; j++)
{
matrix_Cs_J.data[i][j] = Math.Pow(vectorH.data[i], m + j);
}
matrix_Cs_J.data[i][matrix_Cs_J.N - 1] = -1;
}
Matrix matrix_Cs_J_L = new Matrix(n);
Matrix matrix_Cs_J_U = new Matrix(n);
Matrix matrix_Cs_J_P = new Matrix(n);
LUP_decomposition.LUP(matrix_Cs_J, matrix_Cs_J_L, matrix_Cs_J_U, matrix_Cs_J_P);
Vector vector_Cs_J = LUP_decomposition.SLAU(matrix_Cs_J_L, matrix_Cs_J_U, matrix_Cs_J_P, -1 * vectorS);
result = vector_Cs_J.data[2];
tempR = vectorS.data[2] - result;
} while (Math.Abs(tempR) > Eps);
Console.WriteLine($"Count iter: {Math.Pow(L, countIter)}");
return(result);
}
static public double SKF(TypeKF typeKF, ScalarFunk1 f, double defA, double a, double b, double alpha, int n, double h)
{
int k = (Int32)((b - a) / h);
double result = 0.0;
for (int i = 0; i < k; i++)
{
switch (typeKF)
{
case TypeKF.NewtonCots:
result += IKF_NewtonCots(f, defA, a + i * h, a + (i + 1) * h, alpha, n);
break;
case TypeKF.Gauss:
result += KF_Gauss(f, defA, a + i * h, a + (i + 1) * h, alpha, n);
break;
}
}
return(result);
}
static public double AnalysisMethod_Opt(TypeKF typeKF, ScalarFunk1 f, double defA, double a, double b, double alpha, int n, double Eps)
{
double L = 2;
Vector vectorH = new Vector(3);
vectorH.data[0] = b - a;
vectorH.data[1] = vectorH.data[0] / L;
vectorH.data[2] = vectorH.data[1] / L;
//Эйткен
Vector vectorS = new Vector(3);
vectorS.data[0] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[0]);
vectorS.data[1] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[1]);
vectorS.data[2] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[2]);
double m = -Math.Log((vectorS.data[2] - vectorS.data[1]) / (vectorS.data[1] - vectorS.data[0])) / Math.Log(L);
double R = (vectorS.data[2] - vectorS.data[1]) / (Math.Pow(L, m) - 1);
double h_opt = vectorH.data[2] * Math.Pow(Eps / Math.Abs(R), 1.0 / m);
//Чтобы укладывался в отрезок [a, b]
int k = (Int32)Math.Ceiling((b - a) / h_opt);
Console.WriteLine($"Count opt: {k}");
//double logK = Math.Log(k) / Math.Log(L);
//logK = Math.Ceiling(logK);
//k = (int)Math.Pow(L, logK);
vectorH.data[1] = ((b - a) / k) * L * L;
vectorH.data[2] = ((b - a) / k) * L;
if (vectorH.data[1] > (b - a) || vectorH.data[2] > (b - a))
{
Console.WriteLine($"Count iter: {Math.Pow(L, 3)}");
return(vectorS.data[2]);
}
else
{
int countIter = (int)k;
double result = 0.0;
double tempR = Double.PositiveInfinity;
do
{
countIter *= (int)L;
vectorH.data[0] = vectorH.data[1];
vectorH.data[1] = vectorH.data[2];
vectorH.data[2] = vectorH.data[1] / L;
//Эйткен
vectorS.data[0] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[0]);
vectorS.data[1] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[1]);
vectorS.data[2] = SKF(typeKF, f, defA, a, b, alpha, n, vectorH.data[2]);
m = -Math.Log((Math.Abs(vectorS.data[2] - vectorS.data[1])) / (Math.Abs(vectorS.data[1] - vectorS.data[0]))) / Math.Log(L);
//Ричардсон
Matrix matrix_Cs_J = new Matrix(3);
for (int i = 0; i < matrix_Cs_J.N; i++)
{
for (int j = 0; j < matrix_Cs_J.N - 1; j++)
{
matrix_Cs_J.data[i][j] = Math.Pow(vectorH.data[i], m + j);
}
matrix_Cs_J.data[i][matrix_Cs_J.N - 1] = -1;
}
Matrix matrix_Cs_J_L = new Matrix(n);
Matrix matrix_Cs_J_U = new Matrix(n);
Matrix matrix_Cs_J_P = new Matrix(n);
LUP_decomposition.LUP(matrix_Cs_J, matrix_Cs_J_L, matrix_Cs_J_U, matrix_Cs_J_P);
Vector vector_Cs_J = LUP_decomposition.SLAU(matrix_Cs_J_L, matrix_Cs_J_U, matrix_Cs_J_P, -1 * vectorS);
result = vector_Cs_J.data[2];
tempR = vectorS.data[2] - result;
} while (Math.Abs(tempR) > Eps);
Console.WriteLine($"Count iter: {countIter}");
return(result);
}
}